A. The Model

We follow Bloom, Bond, and Van Reenen (2003) in considering a simple dynamic model of firm-level investment, which allows the impact effect of demand growth to vary with the level of uncertainty. The specific model we estimate is an augmented error correction model (ECM) specification of the form:

Here I_it is gross investment by firm i in year t, K_i,t-1 is the net capital stock at the end of the previous year, y_it is the log of real sales, k_it is the log of the capital stock, C_i,t-1 is cash flow in year t — 1, and σ_it is a measure of uncertainty.

In the long run, this specification relates the firm’s capital stock log-linearly to real sales and to unobserved components that may reflect, for example, the cost of capital or demand and technology conditions. These factors are controlled for by the inclusion of year-specific intercepts (α_t) and firm-level “fixed” effects (η_i) in our microeconometric investment model. In the short run, investment rates may depend on recent sales growth and profitability, while a negative parameter θ on the “error correction term” ensures that capital adjusts eventually toward the long-run target.

As shown by Bloom, Bond, and Van Reenen (2003), a key prediction from the analysis of investment under (partial) irreversibility is that the short-run effect of demand shocks on firm-level investment will tend to be smaller for firms facing a higher level of uncertainty. In this specification the interaction term between sales growth and measured uncertainty allows for such heterogeneity in the impact effect of demand shocks, and finding ω₂ < 0 would be consistent with the predicted more cautious response of investment to new information about demand for firms subject to higher uncertainty.²

B. Data Description

The firm-level dataset is obtained from the Datastream on-line service which covers all companies quoted on the U.K. stock market. Our sample is a subset of that used by Bloom, Bond, and Van Reenen (2003). For this investigation we select firms operating principally in the manufacturing sector for which data is available for a relatively long period, a minimum of 22 years between 1972 and 1997. This choice is the result of a trade-off between two conflicting concerns. On the one hand, a completely balanced sample would make the aggregate analysis simpler. However, such a choice would be very costly in terms of lost observations, since we would end up working either with a much smaller number of firms or with a much shorter time period.³ On the other hand, the aim of maximizing the total number of firm-year observations available would result in a heavily unbalanced panel, further complicating the aggregate analysis in the second part of this study. Our choice to focus on a slightly unbalanced panel of 205 firms remaining in the sample for at least 22 years provides a large number of observations (almost 5,000) covering a long time period (26 years), which allows us to investigate investment behavior from both a panel data and a time-series perspective.

We report in Table 1 some basic descriptive statistics for this panel (text tables are grouped following Section IX). As can be seen, the sample consists mainly of large firms, whose total annual investment expenditure is typically the outcome of many underlying investment decisions for multiple types of capital, production lines, plants, and subsidiaries. Importantly, the model developed by Bloom, Bond, and Van Reenen (2003) is robust to these aggregation issues, and indicates that (partial) irreversibility at the level of the underlying investment decisions can have important implications for firm-level investment dynamics, even though zero investment is almost never observed in annual data on large U.K. firms.

Table 1.

Descriptive Statistics - Firm Panel

Note: The sample consists of 205 firms and a total of 4,918 observations.

Table 1.

Descriptive Statistics - Firm Panel

Variable	Mean	Std.Dev.	Median
Investment Rate (Iit/Ki,t–1)	0.123	0.113	0.102
Real Sales Growth (Δyit)	0.024	0.147	0.026
Std. Dev. of Share Returns (σit)	1.377	0.655	1.244
Cash Flow (Cit/Ki,t–1)	0.201	0.184	0.167
Employment	18,774	34,199	5,936
Investment as a Share of Sales (Iit/Yit)	0.049	0.058	0.037
Observations per firm	24	1.714	24

Note: The sample consists of 205 firms and a total of 4,918 observations.

View Table

Table 1.

Descriptive Statistics - Firm Panel

Variable	Mean	Std.Dev.	Median
Investment Rate (Iit/Ki,t–1)	0.123	0.113	0.102
Real Sales Growth (Δyit)	0.024	0.147	0.026
Std. Dev. of Share Returns (σit)	1.377	0.655	1.244
Cash Flow (Cit/Ki,t–1)	0.201	0.184	0.167
Employment	18,774	34,199	5,936
Investment as a Share of Sales (Iit/Yit)	0.049	0.058	0.037
Observations per firm	24	1.714	24

Note: The sample consists of 205 firms and a total of 4,918 observations.

Table 2.

Descriptive Statistics - Manufacturing Sector

Note: The sample covers the period from 1972 to 1997.

Table 2.

Descriptive Statistics - Manufacturing Sector

Variable	Mean	Std.Dev.	Median
Net Investment Rate (It/Kt−1)	0.006	0.024	0.0058
Real Value Added Growth (Δyt)	0.008	0.041	0.0145
Std. Dev. of Share Returns (σt)	2.650	2.000	1.735
Financial Conditions (FINt)	0.041	0.019	0.0375

Note: The sample covers the period from 1972 to 1997.

View Table

Table 2.

Descriptive Statistics - Manufacturing Sector

Variable	Mean	Std.Dev.	Median
Net Investment Rate (It/Kt−1)	0.006	0.024	0.0058
Real Value Added Growth (Δyt)	0.008	0.041	0.0145
Std. Dev. of Share Returns (σt)	2.650	2.000	1.735
Financial Conditions (FINt)	0.041	0.019	0.0375

Note: The sample covers the period from 1972 to 1997.

Our firm-level measure of uncertainty (σ_it) is the annual standard deviation of a firm’s daily share returns, along the lines of previous studies such as Leahy and Whited (1996) and Bloom, Bond, and Van Reenen (2003).⁴ This provides a time-varying measure of uncertainty that reflects many aspects of the firm’s environment, and has been found to be informative about investment behavior in those earlier studies.

C. Empirical Results

The estimation of equation (1) on this dataset requires methods for dynamic panel data models. Blundell and Bond (1998) have developed a generalized methods of moments (GMM) system estimator that, while controlling for the presence of unobserved firm-specific effects, can significantly improve on the efficiency of the basic Arellano and Bond (1991) first-differenced estimator.

The validity of the instruments used is assessed by means of a Sargan test of overidentifying restrictions. Our preferred results here treat sales, cash flow, and measured uncertainty as predetermined variables, in order to ensure consistency with the aggregate analysis performed in the second part of the paper. However, while the particular results reported in this section are used as the benchmark for the subsequent aggregate analysis, the main findings were found to be robust to different choices of the instrument set or to alternative specifications of the dynamic econometric model.⁵

Table 3 reports one-step GMM estimates.⁶ Overall the diagnostic tests appear satisfactory, with no evidence of second-order serial correlation in the first-differenced residuals,⁷ and no rejection of the overidentifying restrictions at standard significance levels. Despite differences in the samples and econometric specifications, our basic results are very similar to those reported by Bloom, Bond, and Van Reenen (2003). Firm-level investment dynamics are well described by an error correction model in which investment responds to sales growth and cash flow in the short run,⁸ and adjusts toward a target for the capital stock that is proportional to real sales in the long run.

Table 3.

Firm-Level Investment Equation

(One-Step GMM Estimates)

Notes: Asymptotic standard errors robust to heteroskedasticity and serial correlation are reported below the coefficients; estimation by GMM-SYSTEM using DPD98 for GAUSS one-step results; full set of time dummies included; “Sargan” is a Sargan-Hansen test of overidentifying restrictions (p-value reported); “LM(2)” is the test statistic for the absence of 2nd order serial correlation in the first-differenced residuals, distributed N(0,1) under the null (p-value reported); “Wald” is a test for the joint significance of time dummies (p-value reported); instruments are y_i,t-1, y_i,t-2, y_i,t-3, (k − y)_i,t−2, C_i,t-1/K_i,t-2, C_i,t-2/K_i,t-3,σ_i,t-1, σ_i,t-2 in the differenced equations, and ${\Delta }\left(\frac{I_{i,t-1}}{K_{i,t-2}}\right)$ in the levels equations.

Table 3.

Firm-Level Investment Equation

(One-Step GMM Estimates)

Iit/Ki,t−1	Parameter Estimates
Δyit	0.4291 0.1071
Δyi,t–1	0.1051 0.0207
(k − y)i,t−2	−0.0963 0.0190
Ci,t−1/Ki,t−2	0.0493 0.0270
σit * Δyit	−0.1300 0.0538
Sargan (p)	0.78
LM2 (p)	0.78
Wald (p)	0.00
Observations	4918
Firms	205

Notes: Asymptotic standard errors robust to heteroskedasticity and serial correlation are reported below the coefficients; estimation by GMM-SYSTEM using DPD98 for GAUSS one-step results; full set of time dummies included; “Sargan” is a Sargan-Hansen test of overidentifying restrictions (p-value reported); “LM(2)” is the test statistic for the absence of 2nd order serial correlation in the first-differenced residuals, distributed N(0,1) under the null (p-value reported); “Wald” is a test for the joint significance of time dummies (p-value reported); instruments are y_i,t-1, y_i,t-2, y_i,t-3, (k − y)_i,t−2, C_i,t-1/K_i,t-2, C_i,t-2/K_i,t-3,σ_i,t-1, σ_i,t-2 in the differenced equations, and ${\Delta }\left(\frac{I_{i,t-1}}{K_{i,t-2}}\right)$ in the levels equations.

View Table

Table 3.

Firm-Level Investment Equation

(One-Step GMM Estimates)

Iit/Ki,t−1	Parameter Estimates
Δyit	0.4291 0.1071
Δyi,t–1	0.1051 0.0207
(k − y)i,t−2	−0.0963 0.0190
Ci,t−1/Ki,t−2	0.0493 0.0270
σit * Δyit	−0.1300 0.0538
Sargan (p)	0.78
LM2 (p)	0.78
Wald (p)	0.00
Observations	4918
Firms	205

Notes: Asymptotic standard errors robust to heteroskedasticity and serial correlation are reported below the coefficients; estimation by GMM-SYSTEM using DPD98 for GAUSS one-step results; full set of time dummies included; “Sargan” is a Sargan-Hansen test of overidentifying restrictions (p-value reported); “LM(2)” is the test statistic for the absence of 2nd order serial correlation in the first-differenced residuals, distributed N(0,1) under the null (p-value reported); “Wald” is a test for the joint significance of time dummies (p-value reported); instruments are y_i,t-1, y_i,t-2, y_i,t-3, (k − y)_i,t−2, C_i,t-1/K_i,t-2, C_i,t-2/K_i,t-3,σ_i,t-1, σ_i,t-2 in the differenced equations, and ${\Delta }\left(\frac{I_{i,t-1}}{K_{i,t-2}}\right)$ in the levels equations.

Table 4.

Manufacturing-Sector Investment Equation

(OLS Estimates)

Notes: Standard errors are reported below the coefficients; estimation by OLS; constant and linear time trend included; “Serial Correlation” is the Lagrange multiplier test of residual first-order serial correlation (p-value reported); “Functional Form” is the Ramsey RESET test using the square of the fitted values (p-value reported); “Normality” is based on a test of skewness and kurtosis of residuals (p-value reported); “Heteroskedasticity” is based on the regression of squared residuals on squared fitted values (p-value reported).

Table 4.

Manufacturing-Sector Investment Equation

(OLS Estimates)

${\left(\frac{I_t}{K_{t-1}}\right)}^{ONS}$	Parameter Estimates
${\Delta }{y}_t^{ONS}$	0.0045 0.0840
${\Delta }{y}_{t-1}^{ONS}$	0.1486 0.0629
${(k-y)}_{t-2}^{ONS}$	−0.1822 0.0326
$FI{N}_{t-1}^{ONS}$	−0.1577 0.0137
${\sigma }_t^{ONS}*{\Delta }{y}_t^{ONS}$	0.0255 0.0307
Serial Correlation (p)	0.00
Functional Form (p)	0.00
Normality (p)	0.08
Heteroskedasticity (p)	0.90

Notes: Standard errors are reported below the coefficients; estimation by OLS; constant and linear time trend included; “Serial Correlation” is the Lagrange multiplier test of residual first-order serial correlation (p-value reported); “Functional Form” is the Ramsey RESET test using the square of the fitted values (p-value reported); “Normality” is based on a test of skewness and kurtosis of residuals (p-value reported); “Heteroskedasticity” is based on the regression of squared residuals on squared fitted values (p-value reported).

View Table

Table 4.

Manufacturing-Sector Investment Equation

(OLS Estimates)

${\left(\frac{I_t}{K_{t-1}}\right)}^{ONS}$	Parameter Estimates
${\Delta }{y}_t^{ONS}$	0.0045 0.0840
${\Delta }{y}_{t-1}^{ONS}$	0.1486 0.0629
${(k-y)}_{t-2}^{ONS}$	−0.1822 0.0326
$FI{N}_{t-1}^{ONS}$	−0.1577 0.0137
${\sigma }_t^{ONS}*{\Delta }{y}_t^{ONS}$	0.0255 0.0307
Serial Correlation (p)	0.00
Functional Form (p)	0.00
Normality (p)	0.08
Heteroskedasticity (p)	0.90

Notes: Standard errors are reported below the coefficients; estimation by OLS; constant and linear time trend included; “Serial Correlation” is the Lagrange multiplier test of residual first-order serial correlation (p-value reported); “Functional Form” is the Ramsey RESET test using the square of the fitted values (p-value reported); “Normality” is based on a test of skewness and kurtosis of residuals (p-value reported); “Heteroskedasticity” is based on the regression of squared residuals on squared fitted values (p-value reported).

We stress two features of these results that are important for our analysis. First, we reject the null hypothesis that the response of investment to sales growth is common to all firms, finding a significantly weaker impact effect for firms subject to higher uncertainty. As predicted by models of (partial) irreversibility, uncertainty plays an important role in shaping investment dynamics. Second, we find that year dummies are highly significant explanatory variables. In common with many microeconometric specifications, this model of firm-level investment is therefore controlling for the effects of a range of unspecified macroeconomic factors, including, for example, interest rates, inflation, taxes, technical progress, and business cycle influences.

A. The Model

In this section, we estimate a simple aggregate counterpart to equation (1), using annual time-series data available for the entire U.K. manufacturing sector. The model estimated is:

where the superscript ONS indicates that the data come from aggregate sources described in the next section. In this case investment (I_t) is measured net of (assumed) depreciation and retirements. FIN_t-1 denotes the percentage of firms reporting that their investment spending is limited by the availability of finance in response to surveys conducted in year t — 1. We include this as a proxy for financial conditions, given that no aggregate cash flow data are available for the manufacturing sector as a whole. More importantly, our aggregate investment model controls for unobserved macroeconomic factors only to the extent that these are proxied by an intercept (c) and a linear trend (t).

B. Data Description

Data on investment, capital stock, and output used in this aggregate specification are obtained from the U.K. Office of National Statistics (ONS) and cover the whole manufacturing sector.⁹ These annual data cover the same period, 1972-1997, as our firm panel. Table 2 reports some basic descriptive statistics. The mean net investment rate is less than 1 percent, indicating very low growth of the U.K. manufacturing capital stock over this period. The average annual growth rate of real manufacturing value added is also below 1 percent. Other sectors of the U.K. economy enjoyed stronger investment and faster output growth over the same period.¹⁰

Our measure of uncertainty here is the annual standard deviation of daily returns on the FTSE Index for the U.K. nonfinancial sector. This includes, but is not limited to, quoted firms in the manufacturing sector. As noted above, our liquidity variable here is a survey measure that was also used by Bean (1981) in his econometric analysis of U.K. manufacturing investment, and is described in Appendix II.

The aggregate data sources available at the manufacturing level differ in potentially important ways, with respect to both concepts and coverage, from those used in our firm-level model. For example, here we use real value added rather than real sales, and net investment rather than gross investment. Our firm-level investment data cover worldwide investment undertaken by manufacturing firms quoted on the London Stock Exchange, including investment by their foreign subsidiaries outside the U.K.; while the ONS aggregate data covers all manufacturing investment in the U.K., including that undertaken by unquoted companies and by U.K. subsidiaries of foreign firms. We will explore the importance of these data differences in Section VI below. For the moment, we also ignore differences in the econometric methods used in our panel data and time-series analyses.

C. Empirical Results

Table 4 reports ordinary least squares (OLS) estimates of equation (2).¹¹ Here the diagnostic tests indicate serious problems, indicating the presence of autocorrelation in the residuals as well as rejection of the functional form we have imposed. These results point to important misspecifications of the model estimated at the aggregate level.

Furthermore, while there is again evidence that investment responds to output growth and liquidity, and adjusts in the direction of a long-run target for the capital stock, in this case we find no evidence that the impact effect of output growth varies with the level of uncertainty. The coefficient on the interaction term between sectoral uncertainty and output growth has the opposite sign to that found in our firm-level model, and is insignificantly different from zero. The same result was found in aggregate specifications that considered different timings (for example,${\sigma }_{t-1}^{ONS}{\Delta }{y}_t^{ONS}$ and ${\sigma }_{t-1}^{ONS}{\Delta }{y}_{t-1}^{ONS}$),and in specifications that added the lagged level of measured uncertainty $\left({\sigma }_{t-1}^{ONS}\right)$ to equation (2).¹²

Based on this preliminary evidence, the investment model that was successfully estimated on micro data appears to be soundly rejected at this more aggregated level. For this or other reasons, the evidence that uncertainty shapes firm-level investment dynamics is not reproduced in our specification for the manufacturing sector. These differences may reflect several factors, including data and estimation differences, and biases due to aggregation. In the rest of this paper we investigate the sources that may have generated this apparently inconsistent empirical evidence.

A. Estimating the Common Time-Varying Shocks

To illustrate this, we can obtain estimates of the common aggregate shocks (α_t) from the microeconometric investment equation presented in Section II. The GMM system estimator identifies the intercept for each period in which equation (1) is observed.¹³ Figure 1 plots these estimates of the common time-varying shocks that influence the investment rates of our sample of U.K. manufacturing firms. As can be seen, this series is countercyclical, with peaks occurring in 1975, 1980, and 1990 when the U.K. economy experienced recessions. Importantly, this series will not be well proxied by the inclusion of a simple linear trend in our aggregate specification. Since the key explanatory variables in our aggregate model (e.g., output growth, profitability, and measured uncertainty) also exhibit clear cyclical patterns, the omission of a good proxy for unobserved common influences is likely to generate important omitted variable biases in the results for aggregate specifications. We illustrate this further in the empirical analysis reported in the following Sections.

Common Time-Varying Shocks

Citation: IMF Working Papers 2005, 158; 10.5089/9781451861778.001.A001

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Common Time-Varying Shocks

Citation: IMF Working Papers 2005, 158; 10.5089/9781451861778.001.A001

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Common Time-Varying Shocks

Citation: IMF Working Papers 2005, 158; 10.5089/9781451861778.001.A001

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A. The Model

In this Section, we consider the importance of different data sources in accounting for the different results obtained in our investment equations for manufacturing firms and for the manufacturing sector as a whole, presented in Sections II and III, respectively. We noted several inconsistencies in the definitions and coverage of the company accounts data and the ONS macro data. To eliminate these, we can use the firm-level data to construct aggregate counterparts to the basic variables included in our microeconometric investment model. This ensures both that the definitions of our constructed aggregate data are identical to the definitions used in our micro data, and that the constructed aggregate data refers to the same population of firms.

To implement this, the specification in equation (8) is particularly helpful. By expressing the relevant variables in terms of their weighted averages computed across the sample of firms observed for each period, this allows us to work with the unbalanced panel of firms considered in Section II.¹⁴ For example, the weighted average figure for real sales growth between periods t — 1 and t included in the specification below is constructed as a weighted average of the individual growth rates for all firms for which we have data in both periods t — 1 and t.

Accordingly, the aggregate specification we estimate under observed aggregation is:

where c is a constant, t is a linear trend, $\begin{array}{l}{\left(I_t/K_{t-1}\right)}^{OA}={\displaystyle {\sum }_{i=1}^N{w}_{K,i,t}\left(I_{it}/K_{i,t-1}\right)}\end{array}$,$\Delta y_t^{OA}={\displaystyle {\sum }_{i=1}^N{w}_{y,i,t}\Delta {In}}{Y}_{it}$,${\left(K-y\right)}_{t-2}^{OA}={\displaystyle {\sum }_{i=1}^N\left(w_{y,i,t-1}\left({In}\left(K_{i,t-2}\right)-Y_{i,t-2,}\right)\right)}$, $\begin{array}{l}{\left(C_{t-1}/K_{t-2}\right)}^{OA}={\displaystyle {\sum }_{i=1}^N{w}_{k,i,t-1}}\left(C_{i,t-1}/K_{i,t-2}\right)\end{array}$, and u_t is an error term. Equation (11) again allows the impact effect of demand growth to vary with the level of measured uncertainty. Our aggregate measure of uncertainty $\left({\sigma }_t^{OA}\right)$ is constructed here as ${\sigma }_t^{OA}={\displaystyle {\sum }_{i=1}^N\left(\frac{m{v}_{it}}{{\displaystyle {\sum }_{j=1}^{N}m{v}_{jt}}}\right){\sigma }_{it}.}$. This is a weighted average of the firm-specific uncertainty measures σ_it, using market weights, where mv_it is the market value of firm i at time t.

B. Empirical Results

Column (1) of Table 5 reports OLS estimates of equation (11). Although the diagnostic tests do not reject this specification as strongly as was the case for our aggregate investment equation using the ONS data for the U.K. manufacturing sector (Table 4), important aspects of the estimated coefficients are still unsatisfactory. The only coefficient that is correctly signed and statistically significant is that on the cash flow term, while the coefficient on the error correction term is statistically significant but incorrectly signed. This specification suggests no short-run effect of real sales growth on investment, and perhaps not surprisingly in view of this, finds no evidence that this impact effect varies with the level of uncertainty.

Table 5.

Aggregate Investment Equations - Observed Aggregation

(OLS Estimates)

Notes: Standard errors are reported below the coefficients; estimation by OLS; constant included; “Serial Correlation” is the Lagrange multiplier test of residual first-order serial correlation (p-value reported); “Functional Form” is the Ramsey RESET test using the square of the fitted values (p-value reported); “Normality” is based on a test of skewness and kurtosis of residuals (p-value reported); “Heteroskedasticity” is based on the regression of squared residuals on squared fitted values (p-value reported).

Table 5.

Aggregate Investment Equations - Observed Aggregation

(OLS Estimates)

(It/Kt-1)OA	(1)	(2)
${\Delta }{y}_t^{OA}$	−0.0742 0.2371	0.1935 0.1707
${\Delta }{y}_{t-1}^{OA}$	−0.0831 0.0723	0.0963 0.0464
${\left(k-y\right)}_{t-2}^{OA}$	0.0664 0.0271	−0.1161 0.0135
(Ct-1/Kt-2)oA	0.9919 0.2877	-0.1445 0.1324
$\left({\sigma }_t^{OA}*{\Delta }{y}_t^{OA}\right)$	0.0736 0.1725	−0.0323 0.1200
t	−0.0079 0.0023	-
αt	-	1.1118 0.1614
Serial Correlation (p)	0.17	0.99
Functional Form (p)	0.09	0.40
Normality (p)	0.14	0.69
Heteroskedasticity (p)	0.29	0.55

Notes: Standard errors are reported below the coefficients; estimation by OLS; constant included; “Serial Correlation” is the Lagrange multiplier test of residual first-order serial correlation (p-value reported); “Functional Form” is the Ramsey RESET test using the square of the fitted values (p-value reported); “Normality” is based on a test of skewness and kurtosis of residuals (p-value reported); “Heteroskedasticity” is based on the regression of squared residuals on squared fitted values (p-value reported).

View Table

Table 5.

Aggregate Investment Equations - Observed Aggregation

(OLS Estimates)

(It/Kt-1)OA	(1)	(2)
${\Delta }{y}_t^{OA}$	−0.0742 0.2371	0.1935 0.1707
${\Delta }{y}_{t-1}^{OA}$	−0.0831 0.0723	0.0963 0.0464
${\left(k-y\right)}_{t-2}^{OA}$	0.0664 0.0271	−0.1161 0.0135
(Ct-1/Kt-2)oA	0.9919 0.2877	-0.1445 0.1324
$\left({\sigma }_t^{OA}*{\Delta }{y}_t^{OA}\right)$	0.0736 0.1725	−0.0323 0.1200
t	−0.0079 0.0023	-
αt	-	1.1118 0.1614
Serial Correlation (p)	0.17	0.99
Functional Form (p)	0.09	0.40
Normality (p)	0.14	0.69
Heteroskedasticity (p)	0.29	0.55

Notes: Standard errors are reported below the coefficients; estimation by OLS; constant included; “Serial Correlation” is the Lagrange multiplier test of residual first-order serial correlation (p-value reported); “Functional Form” is the Ramsey RESET test using the square of the fitted values (p-value reported); “Normality” is based on a test of skewness and kurtosis of residuals (p-value reported); “Heteroskedasticity” is based on the regression of squared residuals on squared fitted values (p-value reported).

Column (2) of Table 5 investigates the importance of omitted variable biases due to the exclusion of common unobserved influences on firm-level investment decisions from this aggregate specification. The simple linear trend is replaced here by the constructed series for α_t that was obtained from our microeconometric model and plotted in Figure 1. As expected, this explanatory variable is highly significant. The inclusion of this term also has an important effect on the remaining parameter estimates. The cash flow term becomes insignificant, while there is now significant evidence of an effect from lagged sales growth, and the error correction term is correctly signed and statistically significant. Importantly, however, we still detect no evidence of significant heterogeneity in the impact effect of sales growth on investment between periods with high and low levels of measured uncertainty.

To summarize, the aggregate investment equations using our constructed analogues of the observed aggregate series do not reproduce parameter estimates that are similar to those obtained using the firm-level panel data. This indicates that differences in the definitions and coverage of the variables are not primarily responsibe for the differences we found when comparing the results using firm-level and aggregate manufacturing datasets. There is some evidence that the exclusion of a good proxy for common unobserved shocks from the aggregate specifications has an important effect on the results, but even controlling for these factors, we are unable to find significant evidence that uncertainty affects short-run investment dynamics when we use the aggregate data in this way.

A. The Model

In this Section, we estimate the relationship between the aggregate series that is implied by exact aggregation of the underlying microeconomic investment equations. To do this, we again make use of the aggregate relationship expressed in terms of averages rather than sums of the microeconomic variables. As shown in equation (7), exact aggregation gives a relationship between the unweighted averages of the firm-level variables. Note that the estimation of this relationship is possible here only because we have the underlying firm-level data to generate these unweighted averages of ratios and growth rates, and would not typically be feasible using published aggregate series.

The aggregate specification we consider under exact aggregation is thus:

Where${\left(I_t/K_{t-1}\right)}^{EA}=\frac{1}{N}{\displaystyle {\sum }_{i=1}^N{I}_{it}/K_{i,t-1}}$,$\Delta y_t^{EA}=\frac{1}{N}{\displaystyle {\sum }_{i=1}^N\Delta {In}{Y}_{it}}$,${\left(k-y\right)}_{t-2}^{EA}=\frac{1}{N}\left({\displaystyle {\sum }_{i=1}^N\left({In}{K}_{i,t-2}-{In}{Y}_{i,t-2}\right)}\right)$,${\left({\sigma }_t*\Delta y_t\right)}^{EA}=\frac{1}{N}{\displaystyle {\sum }_{i=1}^N\left({\sigma }_{it}*\Delta {In}{Y}_{it}\right)}$,${\left(C_t/K_{t-1}\right)}^{EA}=\frac{1}{N}{\displaystyle {\sum }_{i=1}^N{C}_{i,t-1}/K_{i,t-2}}$ and φ_t is an error term.